No abstract

By proving various equivalent versions of the generalized Weyl-von Neumann theorem, we investigate the structure of projections in the multiplier algebra [Formula: see text] of certain C*-algebra [Formula: see text] with real rank zero. For example, we prove that [Formula: see text] if and only if any two projections in [Formula: see text] are simultaneously quasidiagonal. In case [Formula: see text] is a purely infinite simple C*-algebra, [Formula: see text] if and only if any two projections in [Formula: see text] are simultaneously quasidiagonal. If [Formula: see text] is one of the Cuntz algebras, or one of finite factors or type III factors, then any two projections in [Formula: see text] are simultaneously quasidiagonal. On the other hand, if [Formula: see text] is one of the Bunce-Deddens algebras or one of the irrational rotation algebras of real rank zero, then there exist two projections in [Formula: see text] which are not simultaneously quasidiagonal.

No abstract

Many previously observed strong chiroptical effects are limited to chiral metamaterials with complex three-dimensional building blocks. Recently, chiral metamirrors consisting of planar elements are proposed to selectively reflect one particular circularly polarized light (CPL) while absorbing the other, with the reflected one either preserving or altering its spin state. However, they are limited by complicated subwavelength chiral profiles of their unit cells, which are challenging to fabricate in the visible-near-infrared (NIR) region. We present an extrinsically chiral metamirror that reflects one CPL preserving its handedness while strongly absorbing the other, reaching a circular conversion dichroism (CCD) in reflectance as large as 0.43 in the NIR region. Our polarization-conserving mirror possesses an Au pillar array and a continuous Al film separated by a SiO 2 dielectric layer, where the Au pillars are periodically arranged by a rectangular lattice. The rather simple geometry of mirror significantly simplifies its fabrication in the high frequency region. The pronounced CCD originates from a chiral triad of the achiral resonator array and light's propagation direction. Such a chiral mirror provides an efficient methodology toward handedness-selective modulation of the CPL and finds applications in planar photonic devices such as molecular spectroscopy, quantum information, and polarimetric imaging.